Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design

EEG neurofeedback research: A fertile ground for psychiatry?

International audienceThe clinical efficacy of neurofeedback is still a matter of debate. This paper analyzes the factors that should be taken into account in a transdisciplinary approach to evaluate the use of EEG NFB as a therapeutic tool in psychiatry. Neurofeedback is a neurocognitive therapy based on human–computer interaction that enables subjects to train voluntarily and modify functional biomarkers that are related to a defined mental disorder. We investigate three kinds of factors related to this definition of neurofeedback. We focus this article on EEG NFB. The first part of the paper investigates neurophysiological factors underlying the brain mechanisms driving NFB training and learning to modify a functional biomarker voluntarily. Two kinds of neuroplasticity involved in neurofeedback are analyzed Hebbian neuroplasticity, i.e. long-term modification of neural membrane excitability and/or synaptic potentiation, and homeostatic neuroplasticity, i.e. homeostasis attempts to stabilize network activity. The second part investigates psychophysiological factors related to the targeted biomarker. It is demonstrated that neurofeedback involves clearly defining which kind of relationship between EEG biomarkers and clinical dimensions (symptoms or cognitive processes) is to be targeted. A nomenclature of accurate EEG biomarkers is proposed in the form of a short EEG encyclopedia (EEGcopia). The third part investigates human–computer interaction factors for optimizing NFB training and learning during the closed loop interaction. A model is proposed to summarize the different features that should be controlled to optimize learning. The need for accurate and reliable metrics of training and learning in line with human–computer interaction is also emphasized, including targeted biomarkers and neuroplasticity. All these factors related to neurofeedback show that it can be considered as a fertile ground for innovative research in psychiatry